Non-realisability problem with the conventional method of moments in wet-steam flows

• Published in: Proceedings of the Institution of Mechanical Engineers. Part A, Journal of power and energy Journal of power and energy, 2018-08, Vol.232 (5), p.473-489
• Main Authors: Afzalifar, Ali, Turunen-Saaresti, Teemu, Grönman, Aki
• Format: Article
• Language: English
• Subjects: Closures; Finite volume method; Generalized method of moments; Identification methods; Method of moments; Particle size distribution; Simulation; Transport equations
• ISSN: 0957-6509; 2041-2967
• DOI: 10.1177/0957650917735955

The method of moments offers an efficient way to preserve the essence of particle size distribution, which is required in many engineering problems such as modelling wet-steam flows. However, in the context of the finite volume method, high-order transport algorithms are not guaranteed to preserve the moment space, resulting in so-called ‘non-realisable’ moment sets. Non-realisability poses a serious obstacle to the quadrature-based moment methods, since no size distribution can be identified for a non-realisable moment set and the moment-transport equations cannot be closed. On the other hand, in the case of conventional method of moments, closures to the moment-transport equations are directly calculated from the moments themselves; as such, non-realisability may not be a problem. This article describes an investigation of the effects of the non-realisability problem on the flow conditions and moment distributions obtained by the conventional method of moments through several one-dimensional test cases involving systems that exhibited similar characteristics to low-pressure wet-steam flows. The predictions of pressures and mean droplet sizes were not considerably disturbed due to non-realisability in any of the test cases. However, in one case that was characterised by strong temporal and spatial gradients, non-realisability did undermine the accuracy of the predictions of measures for the underlying size distributions, including the standard deviation and skewness.